Question

Which shows a difference of squares?

Answer 1

$16yx^{2} -x^{2}$ shows the difference between two squares

Further Explanation

Quadratic identity  

• An identity is an equation or an expression that is always true for any value. These equations are true no matter the value plugged in for the variable.

In quadratic expression we have quadratic identities which includes;

1. $(a-b)^{2} = a^{2} - 2ab + b^{2}$

2. $(a+b)^{2} = a^{2} + 2ab + b^{2}$

3. $a^{2} -b^{2} =(a-b)(a+b)$

Considering the quadratic identity

$a^{2} -b^{2}$

Which shows the difference between $a^{2}$ and $b^{2}$

We can expand to show the difference between two squares;

$a^{2} -b^{2}$ may be expanded to $(a-b)(a+b)$

Therefore:

$a^{2} -b^{2}$ is an expression known as difference between two squares, and

 $(a-b)$ and $(a+b)$ are the factors of $a^{2} -b^{2}$

Proof of the quadratic identity

$(a-b)(a+b)$

Using distributive property we get;

$a^{2} +ab-ab-b^{2}$

but; $ab-ab=0$

Therefore;

$a^{2} -b^{2} =(a-b)(a+b)$

Conclusion

Difference of two perfect squares = sum of two numbers x Difference of two numbers

That is; $a^{2} -b^{2} =(a-b)(a+b)$

Considering;

$16y^{2} -x^{2}$ is in the form of $a^{2} -b^{2}$

Its factors will be

$4y-x$ and $4y-x$

Keywords: Quadratic dentity, difference between squares

Learn more about:

• Difference between two squares: brainly.com/question/12462696
• Example and explanation: brainly.com/question/12462696

Level: High school

Subject: Mathematics

Topic: Quadratic expressions

Sub-topic: Quadratic identities

Answer 2

16y² - x²   shows the difference of squares.

square root of 16y² is 4y
square root fo x² is x

(4y - x)(4y + x)
4y(4y + x) -x(4y + x)
16y² + 4xy -4xy - x²
16y² - x² 

The middle two terms is equal to zero.